Neural 3D Morphable Models: Spiral Convolutional Networks for 3D Shape Representation Learning and Generation

Generative models for 3D geometric data arise in many important applications in 3D computer vision and graphics. In this paper, we focus on 3D deformable shapes that share a common topological structure, such as human faces and bodies. Morphable Models and their variants, despite their linear formulation, have been widely used for shape representation, while most of the recently proposed nonlinear approaches resort to intermediate representations, such as 3D voxel grids or 2D views. In this work, we introduce a novel graph convolutional operator, acting directly on the 3D mesh, that explicitly models the inductive bias of the fixed underlying graph. This is achieved by enforcing consistent local orderings of the vertices of the graph, through the spiral operator, thus breaking the permutation invariance property that is adopted by all the prior work on Graph Neural Networks. Our operator comes by construction with desirable properties (anisotropic, topology-aware, lightweight, easy-to-optimise), and by using it as a building block for traditional deep generative architectures, we demonstrate state-of-the-art results on a variety of 3D shape datasets compared to the linear Morphable Model and other graph convolutional operators.Comment: to appear at ICCV 201

Screened poisson hyperfields for shape coding

We present a novel perspective on shape characterization using the screened Poisson equation. We discuss that the effect of the screening parameter is a change of measure of the underlying metric space. Screening also indicates a conditioned random walker biased by the choice of measure. A continuum of shape fields is created by varying the screening parameter or, equivalently, the bias of the random walker. In addition to creating a regional encoding of the diffusion with a different bias, we further break down the influence of boundary interactions by considering a number of independent random walks, each emanating from a certain boundary point, whose superposition yields the screened Poisson field. Probing the screened Poisson equation from these two complementary perspectives leads to a high-dimensional hyperfield: a rich characterization of the shape that encodes global, local, interior, and boundary interactions. To extract particular shape information as needed in a compact way from the hyperfield, we apply various decompositions either to unveil parts of a shape or parts of a boundary or to create consistent mappings. The latter technique involves lower-dimensional embeddings, which we call screened Poisson encoding maps (SPEM). The expressive power of the SPEM is demonstrated via illustrative experiments as well as a quantitative shape retrieval experiment over a public benchmark database on which the SPEM method shows a high-ranking performance among the existing state-of-the-art shape retrieval methods

3D object retrieval and segmentation: various approaches including 2D poisson histograms and 3D electrical charge distributions.

Nowadays 3D models play an important role in many applications: viz. games, cultural heritage, medical imaging etc. Due to the fast growth in the number of available 3D models, understanding, searching and retrieving such models have become interesting fields within computer vision. In order to search and retrieve 3D models, we present two different approaches: one is based on solving the Poisson Equation over 2D silhouettes of the models. This method uses 60 different silhouettes, which are automatically extracted from different viewangles. Solving the Poisson equation for each silhouette assigns a number to each pixel as its signature. Accumulating these signatures generates a final histogram-based descriptor for each silhouette, which we call a SilPH (Silhouette Poisson Histogram). For the second approach, we propose two new robust shape descriptors based on the distribution of charge density on the surface of a 3D model. The Finite Element Method is used to calculate the charge density on each triangular face of each model as a local feature. Then we utilize the Bag-of-Features and concentric sphere frameworks to perform global matching using these local features. In addition to examining the retrieval accuracy of the descriptors in comparison to the state-of-the-art approaches, the retrieval speeds as well as robustness to noise and deformation on different datasets are investigated. On the other hand, to understand new complex models, we have also utilized distribution of electrical charge for proposing a system to decompose models into meaningful parts. Our robust, efficient and fully-automatic segmentation approach is able to specify the segments attached to the main part of a model as well as locating the boundary parts of the segments. The segmentation ability of the proposed system is examined on the standard datasets and its timing and accuracy are compared with the existing state-of-the-art approaches

Real-time hand gesture recognition exploiting multiple 2D and 3D cues

The recent introduction of several 3D applications and stereoscopic display technologies has created the necessity of novel human-machine interfaces. The traditional input devices, such as keyboard and mouse, are not able to fully exploit the potential of these interfaces and do not offer a natural interaction. Hand gestures provide, instead, a more natural and sometimes safer way of interacting with computers and other machines without touching them. The use cases for gesture-based interfaces range from gaming to automatic sign language interpretation, health care, robotics, and vehicle automation. Automatic gesture recognition is a challenging problem that has been attaining a growing interest in the research field for several years due to its applications in natural interfaces. The first approaches, based on the recognition from 2D color pictures or video only, suffered of the typical problems characterizing such type of data. Inter occlusions, different skin colors among users even of the same ethnic group and unstable illumination conditions, in facts, often made this problem intractable. Other approaches, instead, solved the previous problems by making the user wear sensorized gloves or hold proper tools designed to help the hand localization in the scene. The recent introduction in the mass market of novel low-cost range cameras, like the Microsoft Kinect, Asus XTION, Creative Senz3D, and the Leap Motion, has opened the way to innovative gesture recognition approaches exploiting the geometry of the framed scene. Most methods share a common gesture recognition pipeline based on firstly identifying the hand in the framed scene, then extracting some relevant features on the hand samples and finally exploiting suitable machine learning techniques in order to recognize the performed gesture from a predefined ``gesture dictionary''. This thesis, based on the previous rationale, proposes a novel gesture recognition framework exploiting both color and geometric cues from low-cost color and range cameras. The dissertation starts by introducing the automatic hand gesture recognition problem, giving an overview of the state-of-art algorithms and the recognition pipeline employed in this work. Then, it briefly describes the major low-cost range cameras and setups used in literature for color and depth data acquisition for hand gesture recognition purposes, highlighting their capabilities and limitations. The methods employed for respectively detecting the hand in the framed scene and segmenting it in its relevant parts are then analyzed with a higher level of detail. The algorithm first exploits skin color information and geometrical considerations for discarding the background samples, then it reliably detects the palm and the finger regions, and removes the forearm. For the palm detection, the method fits the largest circle inscribed in the palm region or, in a more advanced version, an ellipse. A set of robust color and geometric features which can be extracted from the fingers and palm regions, previously segmented, is then illustrated accurately. Geometric features describe properties of the hand contour from its curvature variations, the distances in the 3D space or in the image plane of its points from the hand center or from the palm, or extract relevant information from the palm morphology and from the empty space in the hand convex hull. Color features exploit, instead, the histogram of oriented gradients (HOG), local phase quantization (LPQ) and local ternary patterns (LTP) algorithms to provide further helpful cues from the hand texture and the depth map treated as a grayscale image. Additional features extracted from the Leap Motion data complete the gesture characterization for a more reliable recognition. Moreover, the thesis also reports a novel approach jointly exploiting the geometric data provided by the Leap Motion and the depth data from a range camera for extracting the same depth features with a significantly lower computational effort. This work then addresses the delicate problem of constructing a robust gesture recognition model from the features previously described, using multi-class Support Vector Machines, Random Forests or more powerful ensembles of classifiers. Feature selection techniques, designed to detect the smallest subset of features that allow to train a leaner classification model without a significant accuracy loss, are also considered. The proposed recognition method, tested on subsets of the American Sign Language and experimentally validated, reported very high accuracies. The results showed also how higher accuracies are obtainable by combining proper sets of complementary features and using ensembles of classifiers. Moreover, it is worth noticing that the proposed approach is not sensor dependent, that is, the recognition algorithm is not bound to a specific sensor or technology adopted for the depth data acquisition. Eventually, the gesture recognition algorithm is able to run in real-time even in absence of a thorough optimization, and may be easily extended in a near future with novel descriptors and the support for dynamic gestures